Fast iterative algorithm (FIA) for controlling MEMS deformable mirrors: principle and laboratory demonstration

We present a fast and high accuracy iterative algorithm to control Micro-Electro-Mechanical-System (MEMS) deformable mirrors (DMs) for open-loop (OL) adaptive optics (AO) applications. Our approach relies on a simple physical model for the forces applied on DM actuators and membrane, defined by a small number of parameters that we measure in an experimental setup. The algorithm iteratively applies forces and updates actuator displacements, allowing real-time utilization in an Extreme-AO system (control rate ≥ Khz). Our measurements show that it reproduces Kolmogorov type phase screens with an error equal to 7.3% of the rms of the desired phase (1.6% of the peak-to-valley of the desired phase). This performance corresponds to an improvement of a factor three compared to the standard quadratic model (common relation between voltage and actuator displacement). Originally developed for the DM control of the Subaru Coronagraphic Extreme-AO (SCExAO) project, the algorithm is also suitable for Multi-Object AO systems.